Analytical Model for Failure Strength of Brittle Rocks under Triaxial Compression and Triaxial Extension

Rocks exhibit different failure strengths under triaxial compression and extension. The understanding and quantification of their relationship provide theoretical and practical benefits. Conventional Mohr-type criteria cannot distinguish rock failure strengths under triaxial compression and extension. To overcome this limitation, we present an analytical model based on Mohr failure theory to describe the relationship between the rock failure strengths under triaxial compression and extension in a Mohr plane. Our analytical model indicates that rock failure criteria under both triaxial compression and extension can be expressed in power-law forms. The corresponding strength magnitude and Mohr envelope curvature parameters are analytically determined using measured rock properties from uniaxial tension, uniaxial compression, and equibiaxial compression tests. This model is validated using experimental data of five rock types: granite, marble, basalt, dolomite, and sandstone. Compared with four well-known failure criteria, the proposed model demonstrates the ability to predict the failure strengths of rocks under both triaxial compression and extension.